Conventionally, for example, a method disclosed in Patent Document 1 is known as a method for detecting a flow rate of the blood flowing through a blood vessel, heart, etc., in vivo, on the basis of Doppler signals of the bloodstream detected from ultrasonic echo signals obtained by transmitting and receiving ultrasonic beams to and from a living organism. In the method disclosed in Patent Document 1, the bloodstream is divided into a base flow component and a vortex component for calculation.
On the other hand, Non-Patent Document 1 discloses a method for detecting a blood flow rate within the left ventricle (LV) in the heart. Specifically, this method discloses, as shown in FIG. 5, obtaining two-dimensional color Doppler images 100 and continuous B mode images 200 by a known ultrasonic diagnosis method, and then, obtaining information 101 regarding velocities (Radial Velocities) Vr in the ultrasonic beam direction on the basis of the two-dimensional color Doppler images 100, whereas detecting motion velocities of the left ventricle wall on the basis of the B mode images 200 by a widely known method such as spectrum tracking.
Then, information 102 regarding velocities Vθ in the angular direction perpendicular to the ultrasonic beam direction is obtained using the equation of continuity represented by Formula (1)[Calculation Formula 1]Formula (1)∂θV74(r,θ)=−r∂rVr(r,θ)−Vr(r,θ)  (1)Here,∂xf(x,y)  [Calculation Formula 2]is a simplified expression of
                              ∂                      f            ⁡                          (                              x                ,                y                            )                                                ∂          x                                    [                  Calculation          ⁢                                          ⁢          Formula          ⁢                                          ⁢          3                ]            (the same is true in below).
Specifically, as shown in FIG. 6, in the two-dimensional polar coordinate system (r, θ) with the origin at the ultrasonic beam source T, the motion velocity of the left ventricle wall on one side (for example, the posterior wall) at a radial position r is represented by Vθ−(r), and the motion velocity of the left ventricle wall on the other side (for example, the anterior wall) at the radial position r is represented by Vθ+(r).
Here, the velocity Vθ at a point with a radial position r and an angular position θ (hereinafter referred as a position of interest), in the angular direction perpendicular to the ultrasonic beam direction, may be obtained by integrating Formula (1). The results of the integral according to Formula (1) are a first integral result obtained upon integration from the posterior wall side, and a second integral result obtained upon integration from the anterior wall side. Namely, the first integration can be represented by Formula (2) wherein integration is performed from the position θ—on the posterior wall to the position of interest θ along a line having a constant radial position r (in the angular direction), using the motion velocity Vθ−(r) of the posterior wall as the integral constant.[Calculation Formula 4]Formula (2)Vθ−(r,θ)=Vθ−(r)+∫θ−θ∂θVθ(r,θ)dθ  (2)
The second integration can be represented by Formula (3) wherein integration is performed from the position θ+ on the anterior wall to the position of interest θ along the line having the constant radial position r (in the angular direction), using the motion velocity Vθ+(r) of the anterior wall as the integral constant.[Calculation Formula 5]Formula (3)Vθ+(r,θ)=Vθ+(r)−∫θ−θ+∂θVθ(r,θ)dθ  (3)
As it turns out, two boundary conditions, namely, the condition for the posterior wall side and the condition for the anterior wall side, can be set for a first-order partial differential equation, and as a result, an extra solution is obtained. Accordingly, these solutions are subjected to weighted averaging to reduce error. The velocities Vθ at the position of interest (r, θ), in the angular direction perpendicular to the ultrasonic beam direction, namely, first integral result and the second integral result are subjected to weighted averaging with a weight w, as shown in Formula (4).
                    [                  Calculation          ⁢                                          ⁢          Formula          ⁢                                          ⁢          6                ]                                                            Formula        ⁢                                  ⁢                  (          4          )                                                                                                                                          V                  θ                                ⁡                                  (                                      r                    ,                    θ                                    )                                            =                            ⁢                                                                    wV                    θ                    -                                    ⁡                                      (                                          r                      ,                      θ                                        )                                                  +                                                      (                                          1                      -                      w                                        )                                    ⁢                                                            V                      θ                      +                                        ⁡                                          (                                              r                        ,                        θ                                            )                                                                                                                                              =                            ⁢                                                [                                                                                    wV                                                  θ                          -                                                                    ⁡                                              (                        r                        )                                                              +                                                                  (                                                  1                          -                          w                                                )                                            ⁢                                                                        V                                                      θ                            +                                                                          ⁡                                                  (                          r                          )                                                                                                      ]                                +                                                                                                      ⁢                              [                                                      w                    ⁢                                                                  ∫                                                  θ                          -                                                θ                                            ⁢                                                                                                    ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                θ                                                            )                                                                                                      ⁢                                                  ⅆ                          θ                                                                                                      +                                                            (                                              1                        -                        w                                            )                                        ⁢                                                                  ∫                        θ                                                  θ                          +                                                                    ⁢                                                                                                    ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                θ                                                            )                                                                                                      ⁢                                                  ⅆ                          θ                                                                                                                    ]                                                                        (        4        )            
Here, w represents a weight, and on the basis of the technical common sense, the weight is selected so that the solutions Vθ of Formula (2) and Formula (3) are to be the same. Specifically, the weight is determined as a function of r and 0 representing a position along an integral path, as shown in Formula (5).
                    [                  Calculation          ⁢                                          ⁢          Formula          ⁢                                          ⁢          7                ]                                                            Formula        ⁢                                  ⁢                  (          5          )                                                                                                                        w                ⁡                                  (                                      r                    ,                    θ                                    )                                            =                            ⁢                              1                -                                                                            ∫                                              θ                        -                                            θ                                        ⁢                                                                  [                                                                                                            ∂                              θ                                                        ⁢                                                                                          V                                θ                                                            ⁡                                                              (                                                                  r                                  ,                                  θ                                                                )                                                                                                              -                                                                                    ∂                              θ                                                        ⁢                                                                                          V                                θ                                                            ⁡                                                              (                                                                  r                                  ,                                                                      θ                                    -                                                                                                  )                                                                                                                                    ]                                            ⁢                                              ⅆ                        θ                                                                                                                        ∫                                              θ                        -                                                                    θ                        +                                                              ⁢                                                                  [                                                                                                            ∂                              θ                                                        ⁢                                                                                          V                                θ                                                            ⁡                                                              (                                                                  r                                  ,                                  θ                                                                )                                                                                                              -                                                                                    ∂                              θ                                                        ⁢                                                                                          V                                θ                                                            ⁡                                                              (                                                                  r                                  ,                                                                      θ                                    -                                                                                                  )                                                                                                                                    ]                                            ⁢                                              ⅆ                        θ                                                                                                                                                                    =                            ⁢                                                                    ∫                    θ                                          θ                      +                                                        ⁢                                                            [                                                                                                    ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                θ                                                            )                                                                                                      -                                                                              ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                                                  θ                                  +                                                                                            )                                                                                                                          ]                                        ⁢                                          ⅆ                      θ                                                                                                            ∫                                          θ                      -                                                              θ                      +                                                        ⁢                                                            [                                                                                                    ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                θ                                                            )                                                                                                      -                                                                              ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                                                  θ                                  +                                                                                            )                                                                                                                          ]                                        ⁢                                          ⅆ                      θ                                                                                                                              (        5        )            In addition, when the denominator in Formula (5) becomes closer to “0” and diverged, Formula (5) can be replaced by an approximate Formula (6), wherein ∂θVθ can be obtained by Formula (1).
                    [                  Calculation          ⁢                                          ⁢          Formula          ⁢                                          ⁢          8                ]                                                            Formula        ⁢                                  ⁢                  (          6          )                                                                                                                        w                ⁡                                  (                                      r                    ,                    θ                                    )                                            =                            ⁢                              1                -                                                                            ∫                                              θ                        -                                            θ                                        ⁢                                                                  [                                                                                                            ∂                              θ                                                        ⁢                                                                                          V                                θ                                                            ⁡                                                              (                                                                  r                                  ,                                  θ                                                                )                                                                                                              -                                                                                    min                              ⁡                                                              (                                                                                                      ∂                                    θ                                                                    ⁢                                                                      V                                    θ                                                                                                  )                                                                                      ⁢                                                          (                              r                              )                                                                                                      ]                                            ⁢                                              ⅆ                        θ                                                                                                                        ∫                                              θ                        -                                                                    θ                        +                                                              ⁢                                                                  [                                                                                                            ∂                              θ                                                        ⁢                                                                                          V                                θ                                                            ⁡                                                              (                                                                  r                                  ,                                  θ                                                                )                                                                                                              -                                                                                    min                              ⁡                                                              (                                                                                                      ∂                                    θ                                                                    ⁢                                                                      V                                    θ                                                                                                  )                                                                                      ⁢                                                          (                              r                              )                                                                                                      ]                                            ⁢                                              ⅆ                        θ                                                                                                                                                                    =                            ⁢                                                                    ∫                    θ                                          θ                      +                                                        ⁢                                                            [                                                                                                    ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                θ                                                            )                                                                                                      -                                                                              min                            ⁡                                                          (                                                                                                ∂                                  θ                                                                ⁢                                                                  V                                  θ                                                                                            )                                                                                ⁢                                                      (                            r                            )                                                                                              ]                                        ⁢                                          ⅆ                      θ                                                                                                            ∫                                          θ                      -                                                              θ                      +                                                        ⁢                                                            [                                                                                                    ∂                            θ                                                    ⁢                                                                                    V                              θ                                                        ⁡                                                          (                                                              r                                ,                                θ                                                            )                                                                                                      -                                                                              min                            ⁡                                                          (                                                                                                ∂                                  θ                                                                ⁢                                                                  V                                  θ                                                                                            )                                                                                ⁢                                                      (                            r                            )                                                                                              ]                                        ⁢                                          ⅆ                      θ                                                                                                                              (        6        )            